For high-precision position-measuring tasks in the nanometer range and below, it is not possible to measure the individual axes of a machine sequentially. In such a sequential measuring system, the individual measuring devices for each axis are mounted one upon the other, so that, for example, the stationary part of the second measuring device for the Y-direction is connected to the movable part of the first position-measuring device for the X-direction perpendicular to the Y-direction. The object to be monitored (e.g., a positioning table) is connected to the movable part of the second measuring device. In the guidance for the X-direction, small guidance deviations occur in the Y-direction, as well. However, in a sequential measuring system, such guidance deviations cannot be detected by the second position-measuring device, since it is moved along as a whole with these guidance deviations. Even in the case of very high-quality guidances, deviations of several nanometers can occur transversely to the guidance direction. A high-precision position measurement in several directions using a sequential measurement arrangement is therefore ruled out.
It is necessary to securely join the stationary parts of the measuring devices for all measuring directions to a measuring frame, and the movable parts to the object to be monitored. Only in this manner is it ensured that each measuring device is really able to detect all relevant movements in the respective measuring direction. For example, on the movable object, it is possible to mount scales having optical, magnetic or capacitive graduations that are scanned or read in contactless fashion by corresponding scanning heads attached to the measuring frame. In addition to a high-precision, incremental track, such scales usually include further tracks that contain absolute position information. In the simplest case, this may be a reference mark which, when it is traveled over by the scanning head, is assigned to one signal period of the incremental track, and thereby supplies absolute position information; or it may also be an absolutely coded track which permits the readout of an absolute position in every position of the position-measuring device. Such tracks are denoted hereinafter as absolute tracks. The allocation of the absolute track to the incremental track is important, since only in this manner is it possible to form exact position values.
Generally, the incremental signals resulting from the scanning of the incremental tracks, and usually also the absolute signals resulting from the scanning of the absolute tracks, are able to be acquired and evaluated over a wide tolerance range with respect to the alignment of the scale and the associated scanning head. However, this does not hold true for the assignment of the absolute position information from the absolute track to the relative position information from the incremental track. This assignment is also referred to as the connection of the absolute track to the incremental track. So that one signal period of the associated incremental track may be assigned clearly to each item of absolute information, it is necessary to adhere to quite a small tolerance for the alignment between the scanning head and the allocated scale, this tolerance also being referred to hereinafter as connection tolerance.
When starting up a machine having such a position-measuring system made up of a plurality of position-measuring devices for several degrees of freedom or measuring directions, the problem may arise that initially the alignment of the movable object relative to the measuring frame is only very rough, e.g., by way of mechanical stops. Therefore, during the startup, only a quite large tolerance is provided with respect to the alignment between object and measuring frame, which hereinafter is also referred to as initial tolerance. Too large a scanning distance, or too large a mutual tilt between the scanning heads and the allocated scales, can make the evaluation of the absolute information or its assignment to the incremental track impossible. This is also the case when angle axes are also involved. An initialization of the position-measuring system is therefore very difficult.